Computational Physics
A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent…
Humans can infer accurate mechanical outcomes from only a few observations, a capability known as mechanics intuition. The mechanisms behind such data-efficient learning remain unclear. Here, we propose a reinforcement learning framework in…
A semi-implicit Lax-Wendroff kinetic scheme is developed for hydrodynamic phonon transport in solid materials based on the Boltzmann transport equation under the double relaxation time approximation, in which both the normal and resistive…
Inverse design enables automating the discovery and optimization of devices achieving performance significantly exceeding that of traditional human-engineered designs. However, existing methodologies to inverse-design electromagnetic…
We study fast and reliable generative transport for the 3D KS (Keller-Segel) and KPP (Kolmogorov-Petrovsky-Piskunov) equations in the presence of fluid flows with the goal to approximate the map between initial and terminal distributions…
Rimu.jl is a Julia package for solving many-body quantum problems. The core of the package is a matrix-free implementation of Hamiltonians and other operators and compact representation of Fock states, which together allow for efficient…
Learning reduced descriptions of chaotic many-body dynamics is fundamentally challenging: although microscopic equations are Markovian, collective observables exhibit strong memory and exponential sensitivity to initial conditions and…
Although electrostatics can be incorporated into machine-learned interatomic potentials, existing approaches are computationally very demanding, limiting large-scale, long-time simulations of electrostatics-driven phenomena such as…
We present the novel Tensorized Discontinuous Isogeometric Analysis (TDIGA) method applied to the discontinuous Galerkin (DG) time-independent 2-D linearized Boltzmann transport equation (LBTE) with higher-order scattering, discretized with…
We present a spectral finite-element formulation of the optimized effective potential (OEP) method for atomic structure calculations in the random phase approximation (RPA). In particular, we develop a finite-element framework that employs…
We introduce a smooth B-spline discretization in polar coordinates on the unit disc that corrects the loss of regularity present at the origin caused by the coordinate singularity in standard tensor-product B-spline formulations. The method…
Oscillatory rarefied gas flows are frequently encountered in MEMS, and their efficient numerical simulation remains a major challenge due to the time dependent nature of the problem and the high dimensionality of the Boltzmann kinetic…
Complex dynamical systems frequently encounter a recurrent structural instability: the collapse of the spectral gap, driving the system toward a low-dimensional "Zero-Mode Attractor" (e.g., spectral pile-up or over-smoothing). Building upon…
We present a universal quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than 1/2) Hamiltonians, based on the recently developed permutation matrix representation (PMR) framework. Our approach extends a…
Learning the full family of solutions to parameterized partial differential equations (PDEs) is a central challenge to our ability to model the behavior of heterogeneous systems, with a variety of fundamental and application-oriented…
Oscillator Ising Machines (OIMs) and probabilistic bit (p-bit)-based computing platforms have emerged as promising paradigms for tackling complex combinatorial optimization problems. Although traditionally viewed as distinct approaches,…
Foundation models, or large atomistic models (LAMs), aim to universally represent the ground-state potential energy surface (PES) of atomistic systems as defined by density functional theory (DFT). The scaling law is pivotal in the…
Granular materials subjected to impact loading exhibit highly heterogeneous spatiotemporal dynamics governed by wave propagation, pore collapse, and grain-scale rearrangements. Mesoscale hydrocodes resolve these processes but are…
Foundational machine-learned interatomic potentials have emerged as powerful tools for atomistic simulations, promising near first-principles accuracy across diverse chemical spaces at a fraction of the cost of quantum-mechanical…
The design of spacecraft thermal protection systems (TPS) requires accurate knowledge of thermal transport properties across wide ranges of temperature and pressure. For fibrous insulation, conventional measurement techniques in laboratory…